Powers of i - Problem 2

Simplifying i to a power. In this problem what we’re looking at is i to the negative 273 and there’s a couple of things that we need to take into consideration to begin with.

We know that a negative exponent puts the number in the bottom. So the first I want to do is rewrite this as 1 over i to the 273.

Next thing I want to do is actually simplify whatever i to the 273 is and in order to do that I want to find the nearest multiple of 4 that’s close to 273. In order to do that, we just do division; how many times does 4 go into 273? 4 into 27, 6, 24, 33 4 into 33 gives us 8, 32, subtract so I know I have a remainder of 1. This corresponds to i to the first which tells me I just have an i, sorry, that this statement i to the 273 is the same things as i to the first. Wow I can’t write today, i to the first which is just i. So I have one over i.

We still have an i in the denominator which we’re not allowed to do. So what is till have to do is rationalize this fraction. In order to get rid of i I need to multiply by i over i, end up with i over i², i² is the same thing as -1 so what I end up with is i over -1 or, -i.

Whenever we’re dealing with i to a negative power the process is the same as dealing with a positive power in terms of finding out what that term is but we still may have to rationalize our denominator when we’re finished.